<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E70">Th87</font></span>: <a NAME="T87"><span class="comment"><font color="firebrick">:: GTARSKI5:87</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="gtarski1.html#V9" title="GTARSKI1:attr.9">satisfying_Tarski-model</a>   <a href="gtarski2.html#NV5" title="GTARSKI2:NV.5">satisfying_Lower_Dimension_Axiom</a>   <a href="gtarski1.html#L1" title="GTARSKI1:struct.1">TarskiGeometryStruct</a> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">d</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b6">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b6">A</font> <a href="gtarski5.html#R8" title="GTARSKI5:pred.8">is_plane</a>  &amp;  not  <a href="gtarski1.html#R6" title="GTARSKI1:pred.6">Collinear</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">A</font> &amp; <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">A</font> &amp; <font color="Olive" title="b4">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">A</font> &amp;  not <font color="Olive" title="b5">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">A</font> holds <br/> not <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> <a href="gtarski5.html#R10" title="GTARSKI5:pred.10">are_coplanar</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski5.html#T52" target="_self" onmouseover="rs('gtarski5/T52')" onmouseout="rh()">Th52</a></span>;<br/></div></div>
